Determine the range of the function on the interval .

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

Determine the range of the function f(x)=⌊x⌋+sgn(x)f(x)=\lfloor x \rfloor + \mathrm{sgn}(x) on the interval −2≤x<3-2\le x<3. (a) {−3,−2,1,2,3}\{-3,-2,1,2,3\} (b) {−3,−2,0,2,3}\{-3,-2,0,2,3\} (c) {−3,−2,0,1,2,3}\{-3,-2,0,1,2,3\} (d) {−2,−1,0,1,2}\{-2,-1,0,1,2\}

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